## Helpful Resources

**Learn more about:**

- Applications of IRT to PROs
- Computer adaptive testing (an application of IRT)

**See also:**

- A visual guide to item response theory
- A taxonomy of polytomous IRT models by David Thissen and Lynne Steinberg

# Item Response Theory

## Many instruments in HealthMeasures are based on item response theory (IRT). IRT is a family of mathematical models that assumes that responses on a set of items or questions are related to an unmeasured “trait”. An example of such a trait may be physical function. IRT models assume a person’s level on physical function (e.g., high vs. low) will predict that person’s probability of endorsing each specific item.

#### Parameters and Calibration

When applying IRT, instrument developers assign unique values to each item based on how likely people with different levels of the measured trait are to endorse an item. Once these item values (“parameters”) are estimated (“calibrated”) for each item in a questionnaire or item bank, the parameters can be used to score any new response data from any subset of items. To learn more about parameters, please see part 4 of Karon Cook’s video series “Understanding Item Parameters: Difficulty and Discrimination”.

An IRT model estimates how individuals with given trait levels will respond to items with specified characteristics (called parameters). Examples of parameters include item difficulty and item discrimination. Models are classified by:

- The number of item parameters estimated,
- The number of response options (two vs. more than two), and
- The mathematical relationships assumed among item parameters (how the model is parameterized).

IRT models for items that have only two possible response options are called *dichotomous* response models.

IRT models for items that have more than two possible response options are called *polytomous* response models.

#### IRT vs. Classical Test Theory

IRT is often called ‘‘modern psychometric theory’’ to distinguish it from “classical test theory” (CTT).

Scores based on CTT require that participants respond to every item of a measure or that missing responses be imputed. To get a score using CTT you might:

- Sum item response scores
- Calculate the mean of the response scores
- Use some other arithmetic equation to calculate scale score based on item scores

IRT-based scores are estimated based on a probability model that answers this question:

- Given what is known about the items a person responded to and the pattern of the person’s response, what is the most likely level of the trait (domain) being measured?

#### Types of IRT Models used in HealthMeasures

The two IRT models used in health measures are the 1-parameter logistic model and the graded response model.

#### Thresholds vs. Intercepts

The graded response model has two parameters: a slope [a], and either a threshold [b], or an intercept [c]. The threshold is historically most common, as it represents the score where there is a 50% probability of choosing that response. However, most current IRT software use intercepts (which do not have the same interpretability as thresholds). Intercepts are necessary for fitting multidimensional models. Unidimensional models, such as those used by HealthMeasures, can be fit with either parameterization, and can be readily transformed (b=-c/a or c=-a*b).

#### Computer Adaptive Tests

Computer adaptive tests (CATs) are all but impossible without IRT. With IRT, both people and items are given severities or difficulties. A CAT works by asking a question, getting a score based on a person’s response, and asking the next question based on the item that is at approximately the same difficulty as the current score estimate. This process is repeated until a person is asked the maximum number of items allowed for the CAT (generally 12 for HealthMeasures) or until the score is adequately precise (standard error less than 3.0 or 4.0 on the T-score metric for the pediatric and adult banks, respectively). For a visual explanation of CAT, please see part 6 of Karon Cook’s video series “Applications of IRT".

**You can try out a PROMIS CAT here>>**

#### Multidimensional (correlated traits) and Hierarchical (bifactor, testlet, two-tier) Models

HealthMeasures primarily uses the unidimensional graded response model for self-report measures and the dichotomous 1PL model for some performance test of function measures. There are many other models. Some of the newest models recognize that a scale can measure more than one thing, or that some items might reflect the construct of interest and a nuisance methods factor. While these models are not used in HealthMeasures, interested individuals can learn more about them in this Routledge Handbook.

#### Learn More about IRT Through this Educational Web Series

**Conceptual Introduction to Item Response Theory (7 videos) by Karon F. Cook**

Playlist dropdown is in upper left corner of video player below.